K-sample Multiple Hypothesis Testing for Signal Detection

TL;DR

This paper introduces a K-sample multiple hypothesis testing method for signal detection in noisy data, controlling false discovery rate and improving detection power over traditional one-sample tests.

Contribution

It develops a novel K-sample testing framework that enhances signal detection accuracy and FDR control in noisy measurements.

Findings

Controls FDR effectively with K=2

Increases detection power compared to one-sample tests

Validated through extensive experiments

Abstract

This paper studies the classical problem of estimating the locations of signal occurrences in a noisy measurement. Based on a multiple hypothesis testing scheme, we design a K-sample statistical test to control the false discovery rate (FDR). Specifically, we first convolve the noisy measurement with a smoothing kernel, and find all local maxima. Then, we evaluate the joint probability of K entries in the vicinity of each local maximum, derive the corresponding p-value, and apply the Benjamini-Hochberg procedure to account for multiplicity. We demonstrate through extensive experiments that our proposed method, with K=2, controls the prescribed FDR while increasing the power compared to a one-sample test.